Average Error: 5.4 → 5.4
Time: 14.4s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(1 + y \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(1 + y \cdot y\right)
double f(double x, double y) {
        double r323321 = x;
        double r323322 = 1.0;
        double r323323 = y;
        double r323324 = r323323 * r323323;
        double r323325 = r323322 + r323324;
        double r323326 = r323321 * r323325;
        return r323326;
}
↓
double f(double x, double y) {
        double r323327 = x;
        double r323328 = 1.0;
        double r323329 = y;
        double r323330 = r323329 * r323329;
        double r323331 = r323328 + r323330;
        double r323332 = r323327 * r323331;
        return r323332;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.4
Target0.1
Herbie5.4
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.4

    \[x \cdot \left(1 + y \cdot y\right)\]

  2. Final simplification5.4

    \[\leadsto x \cdot \left(1 + y \cdot y\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1 (* y y))))